A phase transition is a transformation between distinct states of matter, such as from quark-gluon plasma to hadronic matter or crystal growth.A phase transition is an abrupt change in the state of a thermodynamic system when external conditions, such as temperature or pressure, change. First-order transitions, like ice melting or water boiling, involve the release or absorption of latent heat and a jump in density. Second-order transitions occur without latent heat but with a sharp change in heat capacity; examples include the disappearance of iron's magnetization upon heating (the Curie point) or the transition to a superconducting state. Near the critical point, where differences between phases vanish, critical phenomena are observed, described by renormalization group theory.
Early experimental research was conducted by James Joule and William Thomson. Thomas Andrews discovered the critical point in 1869. Paul Ehrenfest proposed the classification of transitions in 1933. Lev Landau created a phenomenological theory based on the order parameter in 1937. Lars Onsager provided an exact solution of the two-dimensional Ising model in 1944. Kenneth Wilson developed the renormalization group approach to critical phenomena in 1971. Boltzmann's statistical mechanics laid the foundations for describing phase transitions.
The thermodynamic potential (e.g., Gibbs free energy) determines the stable phase as the global minimum. When parameters change, the minimum point may shift abruptly (first-order transition) or continuously give way to another when stability is lost (second-order). Near the critical point, large-scale fluctuations develop, and mean-field theory breaks down. The renormalization group allows one to compute critical exponents. In quantum systems, phase transitions can occur even at zero temperature due to quantum fluctuations.
The basis of many technologies: metal quenching, semiconductor production, climate modeling, and creation of superconductors.
At the critical point, a liquid and its vapor become indistinguishable: one can observe opalescence—a cloudiness due to intense density fluctuations.
| phi | variable | phase shift — phase radian |
| lambda | variable | wavelength — wavelength metre |
| Delta n | variable | refractive index change — refractive index change |
| L | variable | path length — length metre |


















